Wednesday, April 30, 2008

Malebranche on Mathematics

In a recent discussion of the philosophy of mathematics at "n-Category Cafe", Malebranche shows up in the comments, in the form of the following quotation:

L’étude des mathématiques est la plus pure application de l’esprit à Dieu.

I don't presently have the whole Malebranchean corpus at my fingertips, so although I suspected this is an abbreviated rather than exact quotation (such as one might pull from memory rather than directly from the text), I couldn't rule out an exact reference. But it would be a very Malebranchean thing to say (in a slightly more qualified form), and I did find something very similar to it in The Search after Truth, Book V, Chapter IV:

But very few know with certainty that to know the truth is to be joined to God as far as nature allows, that to contemplate the true idea of things is in a way to possess God Himself, and that the abstract perceptino of certain universal and immutable truths, which determine all particular truths, is achieved by the mind that attaches itself to God and rejects the body. Metaphysics, pure mathematics, and all the universal sciences that determine and contain the particular sciences as the universal being contains all particular beings seem chimerical to almost everyone--to the pious as well as to those who have no love for God. Consequently, I hardly dare claim that in applying itself to these sciences the mind applies itself to God in the purest and most perfect way of which it is capable, and that it is in perceiving the intelligible worlds that these sciences have as their object that God God knows and produces the sensible world that bodies depend on for their life as as minds depend on the intelligible. (Lennon-Olscamp translation, p. 367, my emphasis).

Malebranche says other interesting things about mathematics in the Search. For instance:

One can hardly do without at least a crude smattering and a genral knowledge of mathematics and nature. Everyone should have learned these sciences in his youth; they detach the mind from sensible things, and they prevent it from becoming soft and effeminate. The are rather useful in life, and they even direct our attention toward God; the knowledge of nature causes this in and of itself, and that of mathematics through the distaste that it inspires in us for the false impressions of our senses. (LO 292)

And of geometry:

Geometry, then, should be regarded as a kind of universal science that opens the mind, makes it attentive, and gives it the skill to control the imagination and to draw from it all the help it can give; for with the help of geometry the mind controls the imagination, and a controlled imagination sustains the mind's perception and attention. (LO 429)

And similarly, of the ancient practice of teaching mathematics to the young:

Apparently they knew that arithmetic and algebra extend the scope of the mind and give it a certain acuteness we cannot acquire from other studies, and that geometry rules the imagination so well that it does not easily grow confused. For this faculty of the soul, so necessary for the sciences, acquires through the practice of geometry a certain scope of accuracy that impels and preserves the mind's clear perception even in the most perplexing difficulties. (LO 483)

He then goes on to recommmend a course of study that would cover all the major mathematics known in his day, up to "the new differential and integral calculi, and to the methods drawn from them for the understanding of curved lines."

Examples could be multiplied; mathematics plays a very important role in Malebranche's theological rationalism, both on the rationalist side (since he uses it to mount a powerful challenge against any empiricist approach) and on the theological side (since on his view mathematics studies purely intelligible extension, which is found in God, being God's divine idea of body).

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